After obtaining the key from the wizzrobes, leave the screen with the key instead of using it on the room with the Roc's Feather and Pegasus Boots.
On this screen, perform a Wall-less Gap Skip, and continue to get the moon pearl. Then do a Wall-restricted Gap Skip, and continue the level. Using the key we can directly go to the shovel room (after getting the lamp of course) and complete the level.
Note: The route involves going through the whole level to get enough gems, since skipping the power bracelet makes you miss out on the majority of the gems you can get. This makes the skip not save too much time overall.
The trigger for the Owl CS can by avoided by doing the following movements:
Using FMC you can pass through the fire without dying.
Use the video below for the positioning, and once you FMC to the right position, simply C-right to clip the Links through the fire. (Green's position as well as the position of the others during the FMC is not very precise)
Note: This method is outdated and not recommended.
It is possible to skip the entire village and bypass the flame wall in the east using Zombie Storage:
Note: This method is slower than doing FMC.
The same trick can be done a lot faster by only dying once using the acceleration from a C-Formation to squeeze one dying Link diagonally through the flame wall. It also does not require OoB, which makes this method very consistent:
In the first GBA shadow area there are switches which are intended to be hit by the slingshot, given on the east side of the room. However, you can avoid grabbing it by simply hitting the two end switches with a sword slash and jump attacking the middle one.
It is possible to save the key from the Mini Boss Room and use it to access the Torch Room. By doing so, you can skip the key one would usually get in the Lamp Room.
After you entered the mini-boss room, lure the bat to your left to the middle, then move up and left, to the edge. Get in a C-Formation and charge the hammer, then reunite with L/Y and press L/Y again to call the formation menu. Press A to choose the C-Left formation. If your positioning was correct, you will hit that head thingy and can throw a Link through the passage the next time you visit the shadow area, after you obtained the small key.
In the room after the Wizzrobes it is possible to skip lighting all of the torches. Simply, light three of the four torches which are closer to the center of the room (but save the one next to the stairs for last). Then stand above that one, hold C-right, and light the last torch. Lastly, holding right during the freeze frames (along with C-right) will cause the Links to clip to the stairs.
Put the links in position as in the video. Line up red with the left wall and get close to the edge. Then hold c-right and roll (either mash or time the rolls very well). Holding up-right (between the up and up-right notch) makes the roll timing less precise.